In answer to the question "what inspired the voice of Heath Ledger's Joker?" there has a lot of speculation. The speculated answer is that Heath Ledger was inspired by a 1971 interview with singer Tom Waits. Watch the interview below: 

The resemblance between the voice of Tom Waits and the voice of Ledger's Joker is staggering... but there is no proof that Ledger ever saw the clip himself. I choose to believe that Heath Ledger was inspired by the Tom Waits interview because of this quote from his 2007 interview with Empire:  "It's a combination of reading all the comic books I could that were relevant to the script and then just closing my eyes and meditating on it. I sat around in a hotel in London for about a month, locked myself away, formed a little diary and experimented with voices- it was important to try to find a somewhat iconic voice and laugh.

I believe that Heath Ledger's search for inspiration may have lead him to the Tom Waits interview in the way that it lead him to read the comic books.